Operator-valued and multivariate free Berry-Esseen theorems
Operator Algebras
2012-02-14 v1
Abstract
We address the question of a Berry-Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element. Since we have to deal with in general non-self-adjoint operators, we introduce the notion of matrix-valued resolvent sets and study the behavior of Cauchy transforms on them.
Keywords
Cite
@article{arxiv.1202.2740,
title = {Operator-valued and multivariate free Berry-Esseen theorems},
author = {Tobias Mai and Roland Speicher},
journal= {arXiv preprint arXiv:1202.2740},
year = {2012}
}